The Pattern

In our daily life, we come across many patterns that characterise relations such as brother and sister, father and son, teacher and student. In mathematics also, we come across many relations such as number m is less than number n, line l is parallel to line m, set A is a subset of set B. In all these, What do we notice ?

Why is the concept of function very important in mathematics ?

Suppose A is a set of 2 colours and B is a set of 3 objects, i.e., A = {red, blue}and B = {b, c, s}, where b, c and s represent a particular bag, coat and shirt, respectively. How many pairs of coloured objects can be made from these two sets?

Write the Definition 1

If the three states, Delhi, Madhya Pradesh and Karnataka were making codes for the licence plates of vehicles, with the restriction that the code begins with an element from set A, which are the pairs available from these sets and how many such pairs will there be ?

If (x + 1, y – 2) = (3,1), find the values of x and y

If P = {a, b, c} and Q = {r}, form the sets P × Q and Q × P. Are these two products equal?

Let A = {1,2,3}, B = {3,4} and C = {4,5,6}. Find (i) A × (B ∩ C) (ii) (A × B) ∩ (A × C) (iii) A × (B ∪ C) (iv) (A × B) ∪ (A × C)

If P = {1, 2}, form the set P × P × P.

If R is the set of all real numbers, what do the cartesian products R × R and R × R × R represent?